18.30 (2014)

A subgroup $H$ of a group $G$ is called $\mathbb{P}$-subnormal in $G$ if either $H = G$, or there is a chain of subgroups $H_0 \subset H_1 \subset \dots \subset H_n = G$ such that $|H_i : H_{i-1}|$ is a prime for all $i = 1, \dots, n$. Must a finite group be soluble if every Shmidt subgroup of it is $\mathbb{P}$-subnormal?